Question

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.​

Answer 1

☆ Given

• Radius of 1st circle = R = 8cm
• Radius of 2nd circle = r = 6cm

☆ To Find

• the radius of the circle having area equal to the sum of the areas of the two circles.

Let the radius of required circle = r' cm

ATQ

Area of required circle = r' = Sum of the area of both the circles

Area of 1st circle = πR²

= π × 8²

= 64 π

Area of 2nd circle = πr²

= π × 6²

= 36 π

Now,

Area of required circle = sum of the area of both the circles

Area required circle = Area if 1st circle + area of 2nd circle

Area of required circle = 64 π + 36 π

⇒ πr'² = 100 π

⇒ r'² = 100

⇒ r' = $\sqrt{100}$

⇒ r' = $\sf\green{10}$

Hence, the radius of the required circle = 10cm

#NAWABZAADI

Answer 2

Answer:

Radius of 1st Circle = 8cm

Radius of 1st Circle = 8cm Area of 1st Circle = πr²1

Radius of 2nd Circle= 6cm

Radius of 2nd Circle= 6cm Area of 2nd Circle = πr²2

Area of both circle= πr²1 + πr²2

= π(r²1+r²2)

= 22/7 (8²+6²)

= 22/7 (64+36)

= 22/7×100 = 2200/7 cm²

Area of bigger Circle = 2200/7cm²

πr² = 2200/7

22/7 ×r² = 2200/7

r² = 2200/7

_________

22/7

r² = 2200/7 × 7/22

r²= 100

r = √100

r = 10cm.

Hence, the radius of bigger circle = 10cm